A072890 The 28-cycle of the n => sigma(n)-n process, where sigma(n) is the sum of divisors of n (A000203).

14316, 19116, 31704, 47616, 83328, 177792, 295488, 629072, 589786, 294896, 358336, 418904, 366556, 274924, 275444, 243760, 376736, 381028, 285778, 152990, 122410, 97946, 48976, 45946, 22976, 22744, 19916, 17716, 14316

Offset: 1

Author

Miklos Kristof, Jul 29 2002

Keywords

• fini
• full
• nonn

Comments

Called a "sociable" chain.

One of the two aliquot cycles of length greater than 2 that were discovered by Belgian mathematician Paul Poulet (1887-1946) in 1918 (the second is A072891). They were the only known such cycles until 1965 (see A072892). - Amiram Eldar, Mar 24 2024

References

• Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, New York: Dover Publications, 1964, Chapter IV, pp. 28-29.
• Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B7, p. 95.
• C. Stanley Ogilvy, Tomorrow's math, unsolved problems for the amateur,Oxford University Press, 2nd ed., 1972, p. 113.
• Paul Poulet, La chasse aux nombres I: Parfaits, amiables et extensions, Bruxelles: Stevens, 1929.

Links

• Robert D. Carmichael, Empirical Results in the Theory of Numbers, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; alternative link. See p. 309.
• Leonard Eugene Dickson, History of the Theory of Numbers, Vol. I: Divisibility and Primality, Washington, Carnegie Institution of Washington, 1919, p. 50.
• Paul Poulet, Query 4865, L'Intermédiaire des Mathématiciens, Vol. 25 (1918), pp. 100-101.
• Eric Weisstein's World of Mathematics, Sociable Numbers.
• Wikipedia, Sociable number.

Crossrefs

Cf. A000203, A001065, A072891, A072892.

Programs

Mathematica

NestList[DivisorSigma[1,#]-#&,14316,28] (* Harvey P. Dale, Oct 27 2013 *)

Formula

a(28+n) = a(n).